Instruments for determining true horizontal and vertical range from the carpenter's level and plumb bob which have been used nearly since antiquity through precise opto-mechanical instruments, such as optical transit squares, to electro-mechanical instruments such as gyroscopes. Each type of instrument is adequate for a given application with regard to required precision, speed of measurement, and convenience. The majority of the simpler inclination indicating instruments do not provide a quantitative indication of inclination, but merely whether or not a test surface is level. Such an indication is adequate for constructing relatively small structures, such as residential buildings of several stories or less. However, much greater accuracy is required for building relatively large structures such as skyscrapers, oceangoing vessels, and the like. For the greater accuracy required in building relatively large structures, optical tooling instruments are often used, such as optical transit squares, by means of which critical points, lines, and planes are observed through precise telescopes and related to reference lines or planes. While much greater accuracy can be achieved with such instruments, the actual use of such instruments can be very time consuming. In certain circumstances, there is a need for an inclination sensing instrument which reads out directly and quantitatively without sacrificing accuracy.
Heretofore, inclination sensing instruments have been devised which employ conductance, inductance, and capacitance as operating parameters. Other instruments have been devised which employ optical and gyroscopic principles. One factor which must be considered in each type of instrument is linearity of response whereby, as the inclination of the instrument is varied in constant increments, a signal property such as current, voltage, or frequency also varies in constant increments. One approach to the linearity problem is non-linear calibration, for example, on an analog type meter scale. An analogy of this approach is the non-linear scale found on conventional analog ohmmeters. Another approach to the non-linearity problem is the use of circuitry having non-linear response in the reverse direction to the non-linearity of the sensor signal to compensate therefor. This is somewhat analogous to an audio compression circuit wherein the gain of the circuit is an inverse function of the input level.